Quantum parameter estimation of nonlinear coupling in trilinear Hamiltonian with trapped ions

TL;DR

This paper introduces a quantum sensing method using trapped ions to measure nonlinear coupling between vibrational modes, achieving high precision near the Heisenberg limit through spin-dependent operations and entangled states.

Contribution

It presents a novel quantum measurement technique for nonlinear phonon coupling in trapped ions, utilizing spin states and motional entanglement for enhanced precision.

Findings

Spin-dependent phonon squeezing enables coupling estimation.

Spin-dependent beam splitter operation facilitates parameter measurement.

Measurement precision can reach the Heisenberg limit with entangled states.

Abstract

I propose an efficient method for measuring non-linear coupling between the collective axial breathing mode and the radial rocking mode induced by the mutual Coulomb repulsion in linear ion crystal. The quantum sensing technique is based on the laser induced coupling between one of the vibrational modes and the internal ion's spin states which allows to estimate the non-linear coupling either by measuring the phonon probability distribution or directly be observing the Ramsey-type oscillations of the ion spin states. I show that due to the presence of non-linear phonon coupling the off-resonance interaction between the ion spin states and the axial breathing mode leads to spin-dependent phonon squeezing of the radial rocking mode. Thus the non-linear coupling can be estimated by measuring population distribution of the motional squeezed state. Furthermore, I show that the off-resonance interaction between the spin and the radial rocking mode creates a spin-dependent beam splitter operation between the two vibrational modes. Thus, the parameter estimation can be carried out by detecting the ion spin populations. Finally, I show that the measurement uncertainty precision can reach the Heisenberg limit by using an entangled states between the two collective modes.